Both Bond Bill and Bond Ted have 5.8 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 25

years to maturity

a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price

of these bonds? (A negative answer should be indicated by a minus sign. Do not

round intermediate calculations and enter your answers as a percent rounded to 2

decimal places, e. g., 32.16.)

b. If rates were to suddenly fall by 2 percent instead, what would be the percentage

change in the price of these bonds? (Do not round intermediate calculations and

enter your answers as a percent rounded to 2 decimal places, e. g., 32.16.)

a.

Percentage change in Bill Price = (91.8486 - 100) / 100 = -0.0815 or -8.15%

Percentage change in Bill Price = (78.1448 - 100) / 100 = -0.2186 or -21.86%

b.

Percentage change in Bill Price = (109.0298 - 100) / 100 = 0.0903 or 9.03%

Percentage change in Bill Price = (132.0946 - 100) / 100 = 0.3209 or 32.09%

Explanation:

To calculate the percentage change in the price of both the bonds, we assume that the par value of both the bonds is $100 each.

a.

To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) both Bill and Ted = 100 * 0.058 * 6/12 = $2.9

Total periods (n) - Bill= 5 * 2 = 10

Total periods (n) - Ted= 25 * 2 = 50

As the bonds were previously price at par, the YTM or market interest rate would have been same as the coupon rate. Thus, the old market interest rate was 5.8%. Now as the interest rates have risen by 2% new interest rate will be = 5.8 + 2 = 7.8%

New r or YTM - both Bill and Ted = 7.8% * 6/12 = 3.9% or 0.039

The formula to calculate the price of the bonds today is attached.

Bond Price - Bill = 2.9 * [( 1 - (1+0.039)^-10) / 0.039]  +  100 / (1+0.039)^10

Bond Price - Bill = $91.8486

Percentage change in Bill Price = (91.8486 - 100) / 100 = -0.0815 or -8.15%

Bond Price - Ted = 2.9 * [( 1 - (1+0.039)^-50) / 0.039]  +  100 / (1+0.039)^50

Bond Price - Ted = $78.1448

Percentage change in Bill Price = (78.1448 - 100) / 100 = -0.2186 or -21.86%

b.

As the bonds were previously price at par, the YTM or market interest rate would have been same as the coupon rate. Thus, the old market interest rate was 5.8%. Now as the interest rates have fallen by 2% new interest rate will be = 5.8 - 2 = 3.8%

New r or YTM - both Bill and Ted = 3.8% * 6/12 = 1.9% or 0.019

The formula to calculate the price of the bonds today is attached.

Bond Price - Bill = 2.9 * [( 1 - (1+0.019)^-10) / 0.019]  +  100 / (1+0.019)^10

Bond Price - Bill = $109.0298

Percentage change in Bill Price = (109.0298 - 100) / 100 = 0.0903 or 9.03%

Bond Price - Ted = 2.9 * [( 1 - (1+0.019)^-50) / 0.019]  +  100 / (1+0.019)^50

Bond Price - Ted = $132.0946

Percentage change in Bill Price = (132.0946 - 100) / 100 = 0.3209 or 32.09%

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